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A371183
Lexicographically earliest sequence of distinct terms in which every triple of consecutive digits contains only one pair that is not coprime.
1
1, 2, 4, 3, 8, 9, 22, 5, 6, 21, 20, 10, 7, 17, 71, 70, 12, 23, 24, 14, 25, 26, 13, 31, 30, 15, 51, 50, 16, 27, 28, 18, 29, 32, 33, 19, 34, 38, 39, 42, 52, 41, 40, 100, 102, 103, 104, 105, 106, 107, 108, 109, 130, 120, 122, 54, 43, 35, 36, 53, 37, 62, 55, 44, 56, 45, 46, 58, 47, 48
OFFSET
1,2
MATHEMATICA
pairwiseQ[a_, b_, c_]:=Sort[{CoprimeQ[a, b], CoprimeQ[b, c], CoprimeQ[a, c]}]=={False, True, True}; a[1]=1; a[2]=2; a[3]=4;
a[n_]:=a[n]=Module[{k=1, digits, tab=Table[a[i], {i, 1, n-1}]},
While[digits=Join[Take[Flatten[IntegerDigits[Take[tab, -3]]], -3], IntegerDigits[k]];
MemberQ[tab, k]||Union[pairwiseQ@@@
Table[{digits[[i]], digits[[i+1]], digits[[i+2]]},
{i, 1, Length[digits]-2}]]!={True}, k++]; k]; a/@Range[70]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Ivan N. Ianakiev, Mar 14 2024
STATUS
approved